If you pay the fee your transaction will be included in the Blockchain. If that fee is the equivalent of $0.10, $1, $10, $100, $1000 or more that simply reflects the value of being able to place a transaction on the Bitcoin blockchain.
What is the purpose of bitcoin if transaction fees went to $1000? It's mostly a fucking interbank settlement tool and that's it. The banks would also get rid of it and use their own proprietary settlement tool or token as well. You have to keep in mind that unlike a bank to peon citizen transaction, in interbank settlement they are NOT attempting to rip each other off (usually), so each party would demand an actual real payment and they would use physical metals for settlement like they always do. The other side wouldn't want or accept an imaginary, valueless, digital token as collateral for anything.